A study of dynamics via Mobius conjugacy map on a family of sixth-order modified Newton-like multiple-zero finders with bivariate polynomial weight functions

作者：Geum Young Hee; Kim Young Ik^*; Alberto Magrenan A

来源：Journal of Computational and Applied Mathematics, 2018, 344: 608-623.

DOI：10.1016/j.cam.2018.06.006

• Parameter space
• Mobius map
• Dynamical plane
• Multiple-zero
• Sixth-order
• Conjugacy

A generic family of sixth-order modified Newton-like multiple-zero finders have been proposed in Geum et al. (2016). Among them we select a specific family of iterative methods with uniparametric bivariate polynomial weight functions and study their dynamics by investigating the relevant parameter spaces and dynamical planes, via Mobius conjugacy map applied to a prototype polynomial of the form (z-a)(m) (z-b)(m). The resulting dynamics is best illustrated through a variety of parameter spaces as well as dynamical planes.

• 出版日期2018-12-15